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تسجيل مستخدم جديدBraided Picard groups and graded extensions of braided tensor categories
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We classify various types of graded extensions of a finite braided tensor category $cal B$ in terms of its $2$-categorical Picard groups. In particular, we prove that braided extensions of $cal B$ by a finite group $A$ correspond to braided monoidal $2$-functors from $A$ to the braided $2$-categorical Picard group of $cal B$ (consisting of invertible central $cal B$-module categories). Such functors can be expressed in terms of the Eilnberg-Mac~Lane cohomology. We describe in detail braided $2$-categorical Picard groups of symmetric fusion categories and of pointed braided fusion categories.
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